Parallelogram

Prove that if diagonal of quadrilateral bisect each other then it is parallelogram

Consider the below quadrilateral ABCD in which diagonals bisect each other. Given:ABCD is a quadrilateral.AC & BD are diagonals bisecting each other.Hence, AO = OC and BO = OD. To Prove:Prove that the given quadrilateral is a parallelogram. Proof:Consider triangle AOB and COD; AO = OC (given)∠AOB = ∠COD ( vertically opposite angle)BO = OD …

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Prove that diagonals of parallelogram bisect each other

Consider the below parallelogram ABCD with diagonals AC and BD. Given:We know that opposite sides of parallelogram are equal.AB = CDAD = BC Also in parallelogram, opposite sides are parallel to each other.AB || CDAD || BC To prove:Diagonals bisect each other.AO = OCDO = OB Proof:Consider triangle AOD and BOC. AD = BC (given)∠DAO …

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